2.75% annual interest for a 30-year term on a $600 purchase, compounded annually
1 answer:
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In the table and chart, we have let x represent numbers of Rock CDs and y represent numbers of Rap CDs.
a) The purple dots represent feasible solutions. Their coordinates are listed in the table (for coordinates on the lines) and as a list of points (for points between the lines).
b) The feasible region for total time in hours is shaded blue.
c) The feasible regiion for total cost is shaded red.
d) The overlap of the two regions is shaded purple. The combinations that are feasible are purple dots in that region.
e) The equations used are listed at the left side of the chart. The equations are labeled by color. (≤112 is the cost equation; ≥75 is the hours equation)
ea) The area that is feasible with respect to both constraints is doubly-shaded.
eba) Too much money is spent to the right of the red line.
ebb) Too few hours are used to the left of the blue line.
f) The line for the desired profit is parallel to the "hours" line, but has x-intercept 10 and y-intercept 6. All the points shown except the two on the lower line will give the desired profit.
g) The higher profit line goes through the points (3, 7) and (8, 4). Those two combinations and the points on or near the upper line above y=4 will meet the higher profit requirement.
a) The purple dots represent feasible solutions. Their coordinates are listed in the table (for coordinates on the lines) and as a list of points (for points between the lines).
b) The feasible region for total time in hours is shaded blue.
c) The feasible regiion for total cost is shaded red.
d) The overlap of the two regions is shaded purple. The combinations that are feasible are purple dots in that region.
e) The equations used are listed at the left side of the chart. The equations are labeled by color. (≤112 is the cost equation; ≥75 is the hours equation)
ea) The area that is feasible with respect to both constraints is doubly-shaded.
eba) Too much money is spent to the right of the red line.
ebb) Too few hours are used to the left of the blue line.
f) The line for the desired profit is parallel to the "hours" line, but has x-intercept 10 and y-intercept 6. All the points shown except the two on the lower line will give the desired profit.
g) The higher profit line goes through the points (3, 7) and (8, 4). Those two combinations and the points on or near the upper line above y=4 will meet the higher profit requirement.
Answer:
96.33% probability that everyone who appears for the flight will get a seat
Step-by-step explanation:
I am going to use the binomial approximation to the normal to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
What is the probability that everyone who appears for the flight will get a seat
100 or less people appearing to the flight, which is the pvalue of Z when X = 100. So
has a pvalue of 0.9633
96.33% probability that everyone who appears for the flight will get a seat